Universal unitary holonomies in photonics

Abstract

Non Abelian holonomy, a geometric aspect of quantum mechanics, underpins the geometric formulation of fundamental interactions and plays a vital role in holonomic quantum computation. Photonics is a fertile platform for exploring non-Abelian holonomies. However, universal unitary holonomies are still out of reach. The lack of control over scale phase degrees of freedom hinders the direct quantum simulation of unitary-governed phenomena, such as electron spin, weak isospin, and quantum chromodynamics,as well as the realization of generic geometric quantum gates for holonomic quantum computing. Here we employ artificial gauge fields (AGFs) to introduce complex-valued couplings, synthesizing arbitrary unitary holonomies and enabling generic geometric quantum gates in photonics. Higher dimensional U(m) transformations are experimentally synthesized based on Givens rotations. Our results pave the way for all-geometric-phase approach for both quantum and classical computing in photonics.